A non-aqueous extraction (NAE) process for producing bitumen from oil sands ore can include a multistage bitumen extraction step where paraffinic solvent and deasphalted oil are added at a downstream stage of extraction at solvent-to-bitumen ratios below asphaltene precipitation onset threshold to remove bitumen from the solid mineral material, while the ore is added to a first stage to mix with the solvent-bitumen mixture and produce solvent diluted bitumen. The process includes recovering the solvent diluted bitumen and the solvent diluted tailings from the extraction step. The solvent diluted bitumen is subjected to deasphalting to produce solvent diluted deasphalted bitumen that is used as a source of the paraffinic solvent and deasphalted oil supplied to extraction. The tailings and asphaltene fraction from deasphalting can be subjected to washing and the washed material can then be subjected to sand solvent recovery. The NAE process can be operated within an operating envelop for effective and efficient performance.